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Законы масштабирования дистилляции

Рекомендация для читателей:


Прежде чем погрузиться в детали, советую ознакомиться с двумя отличными статьями инженера из Яндекса (статья 1, статья 2). В них отлично объясняются принципы дистилляции, её применение в промышленных задачах и ключевые практические аспекты. Это идеальный старт для тех, кто только начинает знакомиться с темой.

Однако, если вы, как и я, стремитесь к глубокому пониманию — этого может оказаться недостаточно. В данном обзоре мы пойдём дальше:

  1. Математическая формализация: Разберём более глубако уравнения, лежащие в основе дистилляции, включая функцию потерь с температурным параметром, оптимизацию распределений и законы масштабирования из работы Apple.

  2. Примеры кода: Покажем, как реализовать дистилляцию на практике — от простых моделей на PyTorch до тонкой настройки гиперпараметров.

  3. Нюансы исследований: Ответим на вопросы, оставшиеся за рамками вводных материалов. Например, почему «слишком умный учитель» вредит ученику и как математически обосновать оптимальное соотношение их размеров.

Для кого это?
Если вы хотите не просто использовать дистилляцию «из коробки», а понимать, как и почему она работает — этот разбор для вас. Мы заглянем «под капот» методов, чтобы вы могли осознанно применять их в своих проектах.

Part 1: Knowledge Distillation

Knowledge Distillation (Дистилляция знаний) — это метод обучения моделей-студентов (обычно меньшего размера и менее сложных) путем передачи "знаний" от предварительно обученной модели-учителя (обычно большей и более сложной). Основная идея заключается в том, что модель-учитель, обладающая большей емкостью и обученная на большом объеме данных, может передать не только свои "жесткие" предсказания (например, класс объекта), но и более богатую информацию о распределении вероятностей классов, которую модель-студент может использовать для более эффективного обучения.

Teacher и Student модели:

В парадигме Knowledge Distillation участвуют две основные модели:

  • Teacher (Учитель): Это большая, предварительно обученная модель, которая считается "экспертом" в решении определенной задачи. Учитель уже достиг высокой точности и обладает "знаниями", которые мы хотим передать студенту. Математически учитель представляется как функцияp(y∣x), которая для входных данных xx выдает распределение вероятностей pпо классам y.

  • Student (Студент): Это меньшая, более простая модель, которую мы хотим обучить. Цель студента — научиться имитировать поведение учителя, чтобы достичь сравнимой производительности, но при этом быть более эффективной с точки зрения вычислительных ресурсов, памяти или времени инференса. Студент представляется как функция q_θ​(y∣x), где θ— параметры модели, которые мы оптимизируем в процессе обучения.

Функция потерь (Loss Function) в Knowledge Distillation:

Общая цель Knowledge Distillation — минимизировать разницу между предсказаниями учителя и студента. Это формализуется через функцию потерьL, которая зависит от предсказаний учителяp(y|x) и студента q_{\theta}(y|x). Процесс обучения заключается в поиске оптимальных параметров $\theta$ для студента, которые минимизируют эту функцию потерь:

L(p(y|x), q_{\theta}(y|x)) \rightarrow \min_{\theta}

Это общее выражение, и конкретный вид функции потерь и способ дистилляции определяют различные подходы. Рассмотрим два основных подхода: hard-label и soft-label дистилляцию.

Это общее выражение, и конкретный вид функции потерь и способ дистилляции определяют различные подходы. Рассмотрим два основных подхода: hard-label и soft-label дистилляцию.

Hard-label Distillation для GPT моделей: объяснение на пальцах

Представьте, что у нас есть две модели:

  • Учитель (Teacher): Большая, мощная GPT модель, например, GPT-3 или что-то подобное. Она обладает огромным количеством знаний о языке и мире, и способна генерировать очень качественный и связный текст.

  • Студент (Student): Маленькая, более компактная GPT модель, например, уменьшенная версия GPT или Transformer меньшего размера. Она менее ресурсоемкая, но изначально уступает учителю в качестве генерации текста.

Наша цель - "научить" маленькую модель-студента генерировать текст так же хорошо, как и большая модель-учитель, используя метод Hard-label Distillation.

Шаги Hard-label Distillation в этом контексте:

  1. Генерация "жестких" меток учителем (Большой GPT):

    • Мы берем большой набор текстовых данных (например, обучающую выборку, на которой изначально обучался учитель, или просто большой корпус текстов).

    • Для каждого фрагмента текста (или запроса) из этого набора, мы просим большую модель-учителя сгенерировать текст. В контексте GPT, это означает, что мы подаем учителю входной текст (например, начало предложения или запрос) и просим его сгенерировать продолжение.

    • Учитель генерирует последовательность токенов, которые он считает наиболее вероятными для продолжения данного текста. Эти сгенерированные последовательности токенов и являются нашими "жесткими" метками.

    Пример:

    • Входной текст (запрос): "Столица Франции - это"

    • Учитель (Большая GPT) генерирует: "Париж." (токены: "Па", "ри", "ж", ".")

    • "Жесткая" метка: Последовательность токенов: ("Па", "ри", "ж", ".")

    Мы повторяем этот процесс для большого количества различных входных текстов, получая набор пар: (исходный входной текст, "жесткая" метка - последовательность токенов, сгенерированная учителем).

  2. Обучение студента (Маленький GPT) на "жестких" метках:

    • Теперь у нас есть синтетический датасет, состоящий из пар (исходный входной текст, "жесткая" метка). Мы будем использовать этот датасет для обучения маленькой модели-студента.

    • Мы обучаем студента предсказывать "жесткие" метки, сгенерированные учителем, используя стандартную задачу языкового моделирования. Это означает, что для каждого входного текста мы хотим, чтобы студент генерировал последовательность токенов, максимально похожую на "жесткую" метку, сгенерированную учителем.

    • В процессе обучения мы используем функцию потерь кросс-энтропии. Мы сравниваем распределение вероятностей токенов, предсказанное студентом, с "жесткой" меткой (которая по сути является распределением, где вероятность "правильного" токена равна 1, а всех остальных - 0). Мы стремимся минимизировать эту кросс-энтропию, заставляя студента "подражать" учителю в предсказании токенов.

    В нашем примере, если студент на вход "Столица Франции - это" предсказывает, например, "Лондон", то функция потерь будет высокой, так как "жесткая" метка учителя была "Париж". В процессе обучения студент будет корректировать свои параметры, чтобы в будущем для аналогичных запросов предсказывать "Париж" или что-то очень похожее на предсказание учителя.

Почему маленькая модель может предсказывать те же токены, что и большая?

  • Передача знаний через "жесткие" метки: Хотя Hard-label Distillation и теряет часть информации из распределения вероятностей учителя, она все равно эффективно передает ключевые знания о том, какие токены являются наиболее вероятными в определенных контекстах. Большая модель, будучи хорошо обученной, "знает", какие продолжения текста являются грамматически правильными, семантически уместными и стилистически подходящими. Генерируя "жесткие" метки, она как бы "подсказывает" маленькой модели, какие именно токены нужно предсказывать.

  • Фокус на наиболее важной информации: "Жесткие" метки концентрируются на наиболее вероятных токенах. В языковом моделировании часто бывает так, что для многих контекстов есть один или несколько доминирующих "правильных" продолжений. Hard-label Distillation помогает маленькой модели быстро освоить эти наиболее важные закономерности, игнорируя менее значимые детали, которые могут быть избыточными для достижения хорошего качества генерации.

  • Упрощение задачи обучения: Обучение на "жестких" метках превращает дистилляцию в стандартную задачу обучения с учителем. Это упрощает процесс обучения и позволяет использовать хорошо известные методы и оптимизаторы. Маленькой модели не нужно пытаться воспроизвести все тонкости распределения вероятностей учителя, ей достаточно научиться предсказывать наиболее вероятные токены, что является более простой задачей.

Важно отметить ограничения Hard-label Distillation:

  • Потеря "мягкой" информации: Как и указано в тексте, Hard-label Distillation теряет информацию о вероятностях других классов и "мягких" отношениях между классами. В контексте языковых моделей это означает, что студент может не улавливать все нюансы стиля, семантики и разнообразия, которые присутствуют в распределении вероятностей учителя. Например, учитель может знать, что "Париж" является самым вероятным ответом на "Столица Франции - это", но также понимать, что "Рим" или "Берлин" являются менее вероятными, но все же допустимыми ответами в определенных контекстах. Hard-label Distillation фокусируется только на "Париже", игнорируя эту "мягкую" информацию.

  • Потенциальное ухудшение разнообразия: Из-за фокусировки на "жестких" метках, студент может стать менее разнообразным в своих генерациях, чем учитель. Он может слишком точно копировать наиболее вероятные ответы учителя, упуская возможность генерировать альтернативные, но все еще качественные варианты.

Математическая формализация:

1. Генерация "жестких" меток учителем: Для каждого примераx^{(n)}из обучающей выборки, учительp(y|x)предсказывает распределение вероятностей классов. "Жесткая" меткаy^{(n)}выбирается как класс с максимальной вероятностью, предсказанной учителем. В контексте языков моделей, гдеyпредставляет собой последовательность токенов, учитель генерирует последовательность "жестких" метокy^{(1)}, \ldots y^{(N)}дляNпримеров. Здесьy^{(n)} = (y_1^{(n)}, \ldots, y_{T_n}^{(n)})представляет собой последовательность токенов длинойT_n.

y^{(1)}, \ldots y^{(N)} \sim p(y|x)

В более простом варианте, для классификации, y^{(n)} = \arg\max_{y} p(y|x^{(n)}). В случае последовательностей, учитель может генерировать целые последовательности наиболее вероятных токенов.

2. Обучение студента на "жестких" метках: Студентq_{\theta}(y|x)обучается максимизировать логарифмическую вероятность "жестких" меток, сгенерированных учителем. Это стандартная задача обучения с учителем, где целевыми метками являютсяy^{(1)}, \ldots y^{(N)}. Функция потерь, которую мы минимизируем (или эквивалентно, максимизируем отрицательную потерю), представляет собой ожидание логарифмической вероятности "жестких" меток под распределениемp(y|x)учителя.

\mathbb{E}_{p(y|x)} [\log q_{\theta}(y|x)] \rightarrow \max_{\theta}

В практической реализации, это ожидание аппроксимируется эмпирическим средним по обучающей выборке. Для последовательностей текста, функция потерь выглядит следующим образом:

\frac{1}{N} \sum_{n=1}^{N} \sum_{t=1}^{T_n} \log q_{\theta}(y_t^{(n)}|y_{<t}^{(n)})

Здесь:

* N — количество примеров в обучающей выборке.

* T_n — длина последовательности для $n$-го примера.

* y_t^{(n)} —t-й токен в последовательности "жестких" меток дляn-го примера, сгенерированных учителем.

* y_{<t}^{(n)} = (y_1^{(n)}, \ldots, y_{t-1}^{(n)}) — префикс последовательности доt-го токена.

* q_{\theta}(y_t^{(n)}|y_{<t}^{(n)}) — вероятность предсказания студентомt-го токенаy_t^{(n)} при условии предыдущих токеновy_{<t}^{(n)}, параметризованная\theta.

Эта функция потерь представляет собой кросс-энтропию между распределением "жестких" меток, сгенерированных учителем, и предсказаниями студента. Мы стремимся максимизировать эту величину, что эквивалентно минимизации отрицательной логарифмической правдоподобности или кросс-энтропии.

Преимущества и недостатки Hard-label Distillation:

  • Преимущества: Простота реализации и понимания. Можно использовать стандартные методы обучения с учителем.

  • Недостатки: Потеря информации, содержащейся в распределении вероятностей учителя. "Жесткие" метки содержат только информацию о наиболее вероятном классе, игнорируя вероятности других классов и "мягкие" отношения между классами, которые учитель "знает". Это может ограничить эффективность передачи знаний.

Реализация Hard-label Distillation на основе Open R1

Ниже представлена реализация Hard-label Distillation с использованием подхода, применяемого в проекте Open R1. Процесс разделен на два этапа: генерация данных учителем и обучение ученика.

@misc{openr1,
    title = {Open R1: A fully open reproduction of DeepSeek-R1},
    url = {https://github.com/huggingface/open-r1},
    author = {Hugging Face},
    month = {January},
    year = {2025}
}

Этап 1: Генерация "жестких" меток большой моделью (учителем)

import argparse
from datasets import load_dataset
from typing import Optional, Dict, Any

from distilabel.pipeline import Pipeline
from distilabel.models import vLLM
from distilabel.steps.tasks import TextGeneration

def build_hard_label_pipeline(
    teacher_model: str,
    base_url: str = "http://localhost:8000/v1",
    prompt_column: Optional[str] = None,
    prompt_template: str = "{{ instruction }}",
    temperature: float = 0.0,
    max_new_tokens: int = 4096,
    input_batch_size: int = 32,
) -> Pipeline:
    """
    Description:
    ---------------
        Создает конвейер для генерации "жестких" меток с использованием модели-учителя.

    Args:
    ---------------
        teacher_model: Идентификатор модели-учителя
        base_url: URL сервера vLLM
        prompt_column: Имя колонки в датасете, содержащей входные тексты
        prompt_template: Шаблон для форматирования промптов
        temperature: Температура для генерации (0.0 для "жестких" меток)
        max_new_tokens: Максимальное количество генерируемых токенов
        input_batch_size: Размер батча для входных данных

    Returns:
    ---------------
        Настроенный конвейер Distilabel

    Raises:
    ---------------
        Exception: В случае ошибки настройки конвейера

    Examples:
    ---------------
        >>> pipeline = build_hard_label_pipeline("deepseek-ai/DeepSeek-R1")
        >>> pipeline.run(dataset)
    """
    # Настраиваем параметры генерации с temperature=0 для получения детерминированных ответов
    generation_kwargs: Dict[str, Any] = {
        "max_new_tokens": max_new_tokens,
        "temperature": temperature,
        "top_p": 1.0,
        "do_sample": False,          # Отключаем семплирование для получения "жестких" меток
    }

    with Pipeline(
        name="hard-label-distillation",
        description="Конвейер для генерации 'жестких' меток с использованием модели-учителя",
    ) as pipeline:
        # Настраиваем модель-учителя через vLLM
        teacher = vLLM(
            model=teacher_model,
            tokenizer=teacher_model,
            extra_kwargs={
                "tensor_parallel_size": 1,               # Можно увеличить для больших моделей
                "max_model_len": max_new_tokens + 2048,  # Добавляем запас для контекста
            },
            generation_kwargs=generation_kwargs,
        )

        # Настраиваем шаг генерации текста
        text_generation = TextGeneration(
            llm=teacher,
            template=prompt_template,
            num_generations=1,           # Для "жестких" меток нам нужна только одна генерация
            input_mappings={"instruction": prompt_column} if prompt_column is not None else {},
            input_batch_size=input_batch_size,
        )

    return pipeline

def generate_hard_labels(
    dataset_name: str,
    dataset_split: str = "train",
    teacher_model: str = "deepseek-ai/DeepSeek-R1",
    output_dataset: str = "my-username/hard-label-distill-dataset",
    prompt_column: str = "problem",
    prompt_template: str = "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}: {{ instruction }}",
    max_examples: Optional[int] = None,
    private: bool = False,
) -> Any:
    """
    Description:
    ---------------
        Генерирует "жесткие" метки с использованием модели-учителя и сохраняет результаты как набор данных на HuggingFace Hub.

    Args:
    ---------------
        dataset_name: Имя исходного датасета
        dataset_split: Имя сплита датасета
        teacher_model: Модель-учитель для генерации "жестких" меток
        output_dataset: Имя выходного датасета на HuggingFace Hub
        prompt_column: Имя колонки, содержащей входные данные
        prompt_template: Шаблон для форматирования промптов
        max_examples: Максимальное количество примеров для обработки
        private: Приватный ли выходной датасет

    Returns:
    ---------------
        Датасет с "жесткими" метками

    Raises:
    ---------------
        Exception: В случае ошибки генерации меток

    Examples:
    ---------------
        >>> hard_label_dataset = generate_hard_labels("my-dataset", "train")
        >>> hard_label_dataset.push_to_hub("my-username/hard-label-dataset")
    """
    # Загружаем исходный датасет
    print(f"Загрузка датасета '{dataset_name}' (сплит: {dataset_split})...")
    dataset = load_dataset(dataset_name, split=dataset_split)

    # Ограничиваем количество примеров, если указано
    if max_examples is not None and max_examples < len(dataset):
        dataset = dataset.select(range(max_examples))

    print(f"Создание конвейера для генерации 'жестких' меток с использованием {teacher_model}...")
    pipeline = build_hard_label_pipeline(
        teacher_model=teacher_model,
        prompt_column=prompt_column,
        prompt_template=prompt_template,
    )

    print(f"Запуск конвейера для генерации 'жестких' меток на {len(dataset)} примерах...")
    # Генерируем "жесткие" метки
    hard_label_dataset = pipeline.run(dataset=dataset)

    # Сохраняем результаты на HuggingFace Hub
    if output_dataset:
        print(f"Сохранение результатов в '{output_dataset}'...")
        hard_label_dataset.push_to_hub(output_dataset, private=private)
        print(f"Датасет с 'жесткими' метками успешно сохранен в '{output_dataset}'.")

    return hard_label_dataset

if __name__ == "__main__":
    parser = argparse.ArgumentParser(description="Генерация 'жестких' меток с использованием модели-учителя")
    parser.add_argument("--dataset", type=str, required=True, help="Имя исходного датасета")
    parser.add_argument("--split", type=str, default="train", help="Сплит датасета")
    parser.add_argument("--teacher-model", type=str, default="deepseek-ai/DeepSeek-R1", help="Модель-учитель")
    parser.add_argument("--output-dataset", type=str, required=True, help="Имя выходного датасета")
    parser.add_argument("--prompt-column", type=str, default="problem", help="Колонка с входными данными")
    parser.add_argument("--prompt-template", type=str,
                       default="You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}: {{ instruction }}",
                       help="Шаблон для форматирования промптов")
    parser.add_argument("--max-examples", type=int, default=None, help="Максимальное количество примеров")
    parser.add_argument("--private", action="store_true", help="Сделать выходной датасет приватным")

    args = parser.parse_args()

    generate_hard_labels(
        dataset_name=args.dataset,
        dataset_split=args.split,
        teacher_model=args.teacher_model,
        output_dataset=args.output_dataset,
        prompt_column=args.prompt_column,
        prompt_template=args.prompt_template,
        max_examples=args.max_examples,
        private=args.private,
    )

Этап 2: Обучение модели-ученика на "жестких" метках

import logging
import os
import sys
from dataclasses import dataclass, field
from typing import Optional, Dict, Any

import datasets
import torch
import transformers
from datasets import load_dataset
from transformers import AutoTokenizer, set_seed
from transformers.trainer_utils import get_last_checkpoint

from trl import SFTTrainer, ModelConfig, TrlParser, get_peft_config
from open_r1.configs import SFTConfig
from open_r1.utils.wandb_logging import init_wandb_training

logger = logging.getLogger(__name__)

@dataclass
class HardLabelDistillConfig(SFTConfig):
    """Конфигурация для обучения ученика с использованием Hard-label Distillation."""

    dataset_name: str = field(
        default=None, metadata={"help": "Датасет с 'жесткими' метками, сгенерированными учителем"}
    )
    input_column: str = field(
        default="problem", metadata={"help": "Колонка с входными данными"}
    )
    target_column: str = field(
        default="generation_0", metadata={"help": "Колонка с выходными данными (жесткими метками) учителя"}
    )
    max_seq_length: int = field(
        default=2048, metadata={"help": "Максимальная длина последовательности"}
    )

def train_student_model(config: HardLabelDistillConfig, model_args: ModelConfig) -> None:
    """
    Description:
    ---------------
    Обучает модель-ученика на 'жестких' метках, сгенерированных учителем.

    Args:
    ---------------
        config: Конфигурация обучения
        model_args: Конфигурация модели

    Returns:
    ---------------
        None

    Raises:
    ---------------
        Exception: В случае ошибки обучения модели

    Examples:
    ---------------
        >>> train_student_model(config, model_args)
    """
    # Настраиваем логирование
    logging.basicConfig(
        format="%(asctime)s - %(levelname)s - %(name)s - %(message)s",
        datefmt="%Y-%m-%d %H:%M:%S",
        handlers=[logging.StreamHandler(sys.stdout)],
    )
    log_level = config.get_process_log_level()
    logger.setLevel(log_level)
    datasets.utils.logging.set_verbosity(log_level)
    transformers.utils.logging.set_verbosity(log_level)

    # Устанавливаем сид для воспроизводимости
    set_seed(config.seed)

    # Проверяем наличие последнего чекпоинта
    last_checkpoint: Optional[str] = None
    if os.path.isdir(config.output_dir):
        last_checkpoint = get_last_checkpoint(config.output_dir)
        if last_checkpoint is not None:
            logger.info(f"Найден чекпоинт, продолжаем обучение с {last_checkpoint}")

    # Инициализируем Weights & Biases, если нужно
    if "wandb" in config.report_to:
        init_wandb_training(config)

    # Загружаем датасет с 'жесткими' метками
    logger.info(f"Загрузка датасета с 'жесткими' метками: {config.dataset_name}")
    dataset = load_dataset(config.dataset_name)

    # Подготавливаем входные данные и метки для обучения
    def prepare_dataset(examples: Dict[str, Any]) -> Dict[str, Any]:
        """Форматирует данные для обучения с учителем."""
        return {
            "input_ids": examples[config.input_column],
            "labels": examples[config.target_column],
        }

    # Трансформируем датасет
    dataset = dataset.map(prepare_dataset, batched=True)

    # Загружаем токенизатор
    tokenizer = AutoTokenizer.from_pretrained(
        model_args.model_name_or_path,
        revision=model_args.model_revision,
        trust_remote_code=model_args.trust_remote_code,
    )

    # Настраиваем chat_template, если указан
    if config.chat_template is not None:
        tokenizer.chat_template = config.chat_template

    # Настраиваем параметры модели
    torch_dtype = (
        model_args.torch_dtype if model_args.torch_dtype in ["auto", None] else getattr(torch, model_args.torch_dtype)
    )
    model_kwargs: Dict[str, Any] = dict(
        revision=model_args.model_revision,
        trust_remote_code=model_args.trust_remote_code,
        torch_dtype=torch_dtype,
        use_cache=False if config.gradient_checkpointing else True,
    )
    config.model_init_kwargs = model_kwargs

    # Создаем SFT тренер
    trainer = SFTTrainer(
        model=model_args.model_name_or_path,
        args=config,
        train_dataset=dataset["train"],
        eval_dataset=dataset["validation"] if "validation" in dataset and config.eval_strategy != "no" else None,
        processing_class=tokenizer,
        peft_config=get_peft_config(model_args),
    )

    # Запускаем обучение
    logger.info("Начало обучения модели-ученика...")
    checkpoint: Optional[str] = None
    if config.resume_from_checkpoint is not None:
        checkpoint = config.resume_from_checkpoint
    elif last_checkpoint is not None:
        checkpoint = last_checkpoint

    train_result = trainer.train(resume_from_checkpoint=checkpoint)
    metrics = train_result.metrics
    trainer.log_metrics("train", metrics)
    trainer.save_metrics("train", metrics)
    trainer.save_state()

    # Сохраняем модель
    logger.info(f"Сохранение модели в {config.output_dir}")
    trainer.save_model(config.output_dir)

    # Создаем карточку модели и загружаем на HuggingFace Hub, если нужно
    kwargs: Dict[str, Any] = {
        "dataset_name": config.dataset_name,
        "tags": ["hard-label-distillation", "open-r1"],
    }

    if trainer.accelerator.is_main_process:
        trainer.create_model_card(**kwargs)
        # Восстанавливаем кэш для быстрого инференса
        trainer.model.config.use_cache = True
        trainer.model.config.save_pretrained(config.output_dir)

    # Оцениваем модель, если нужно
    if config.do_eval and "validation" in dataset:
        logger.info("Оценка модели...")
        metrics = trainer.evaluate()
        trainer.log_metrics("eval", metrics)
        trainer.save_metrics("eval", metrics)

    # Загружаем модель на HuggingFace Hub, если нужно
    if config.push_to_hub:
        logger.info("Загрузка модели на HuggingFace Hub...")
        trainer.push_to_hub(**kwargs)

if __name__ == "__main__":
    # Создаем парсер аргументов
    parser = TrlParser((HardLabelDistillConfig, ModelConfig))
    config, model_args = parser.parse_args_and_config()

    # Запускаем обучение
    train_student_model(config, model_args)

Пример использования

# Этап 1: Генерация "жестких" меток с использованием модели-учителя
python hard_label_distill.py \
  --dataset AI-MO/NuminaMath-TIR \
  --teacher-model deepseek-ai/DeepSeek-R1 \
  --output-dataset username/hard-label-math-dataset \
  --prompt-column problem

# Этап 2: Обучение модели-ученика на сгенерированных "жестких" метках
accelerate launch --config_file=recipes/accelerate_configs/zero3.yaml train_student.py \
  --model_name_or_path Qwen/Qwen2.5-1.5B-Instruct \
  --dataset_name username/hard-label-math-dataset \
  --input_column problem \
  --target_column generation_0 \
  --learning_rate 1.0e-5 \
  --num_train_epochs 2 \
  --packing \
  --max_seq_length 4096 \
  --per_device_train_batch_size 8 \
  --gradient_accumulation_steps 4 \
  --gradient_checkpointing \
  --bf16 \
  --output_dir models/Qwen2.5-1.5B-Hard-Label-Distill

II. Soft-label Distillation: Дистилляция с использованием "мягких" меток

Концепция:

Soft-label distillation, предложенная Хинтоном и соавторами в их знаменитой статье "Distilling the Knowledge in a Neural Network" (2015), является более совершенным методом дистилляции знаний. В отличие от Hard-label distillation, этот подход использует не только "жесткие" метки, но и полное распределение вероятностей, предсказанное учителем, в качестве "мягких" меток (soft labels).

"Мягкие" метки содержат значительно больше информации, чем "жесткие", поскольку они отражают уверенность учителя в различных классах и отношения между ними. Например, учитель может предсказать для изображения собаки вероятности [0.8 для "собака", 0.15 для "волк", 0.03 для "лиса", 0.02 для других классов]. Эта информация гораздо богаче, чем просто метка "собака".

Ключевым компонентом метода является "temperature scaling" (масштабирование температуры), который делает распределение вероятностей более "мягким" и информативным путем деления логитов модели на параметр температуры T > 1.

Soft-label Distillation для GPT моделей: объяснение на пальцах

Представьте, что у нас есть две модели:

  • Учитель (Teacher): Большая, мощная GPT модель с 175 миллиардами параметров. Она обладает глубоким пониманием языка и мира.

  • Студент (Student): Компактная GPT модель с 1.5 миллиардами параметров. Намного быстрее и экономичнее, но изначально уступает учителю в качестве.

Наша цель - научить студента генерировать текст так же хорошо, как учитель, используя Soft-label Distillation.

Шаги Soft-label Distillation:

  1. Генерация "мягких" меток учителем:

    • Для запроса "Столица Франции - это" большая модель-учитель не просто выдает "Париж", но вычисляет вероятности для всех возможных следующих токенов:

      • "Париж": 0.92

      • "город": 0.03

      • "Рим": 0.01

      • ... (и тысячи других токенов с малыми вероятностями)

    • Проблема: это распределение слишком "острое" - один токен имеет почти всю вероятность. Чтобы извлечь больше полезных знаний, применяем temperature scaling:

    • Делим логиты на температуру T (например, T = 2.0) перед применением softmax:

      • "Париж": 0.70 (уменьшилось с 0.92)

      • "город": 0.08 (увеличилось с 0.03)

      • "Рим": 0.05 (увеличилось с 0.01)

      • ... (другие токены тоже получают больше вероятности)

    • Эти "смягченные" распределения сохраняют намного больше информации о том, что модель-учитель "знает".

  2. Обучение модели-студента:

    • Студент обучается не только предсказывать правильный токен, но и воспроизводить всё распределение вероятностей учителя.

    • Для этого используется КЛ-дивергенция (или кросс-энтропия) между распределениями учителя и студента.

    • Важно: распределение студента также "смягчается" с той же температурой T для сопоставимости.

    • Функция потерь умножается на T² для компенсации уменьшения градиентов.

  3. Комбинированное обучение:

    • Обычно используется комбинация двух функций потерь:

      • α · (Потери от "мягких" меток) + (1-α) · (Стандартные потери от "жестких" меток)

    • Где α - коэффициент, обычно от 0.5 до 0.9

Почему это работает лучше Hard-label Distillation?

  • "Темные знания" (Dark Knowledge): Как назвал Хинтон, относительные вероятности "неправильных" ответов содержат ценную информацию. Например, если модель путает "собаку" с "волком", но не с "самолетом", это важная информация.

  • Передача неопределенности: Студент учится не только правильным ответам, но и тому, в каких случаях стоит сомневаться.

  • Более богатый сигнал: Вместо одного бита информации на каждый пример (правильный/неправильный класс), студент получает информацию о всем распределении вероятностей.

Математическая формализация:

1. "Мягкие" метки учителя с температурой T:

Еслиz_i- логит для класса (токена)iот учителя, то "мягкая" метка с температурой T:

p_i^T = \frac{\exp(z_i/T)}{\sum_j \exp(z_j/T)}

Разберем каждый элемент формулы:

* p_i^T: Это "мягкая" вероятность дляi-го токена, с учетом температурыT. Именно это распределение вероятностей, сгенерированное учителем, мы будем использовать как "мягкую метку".

* z_i: Это логит (logit) дляi-го токена, выданный моделью-учителем. Логиты - это значения, которые модель выдает перед применением функции softmax. Они представляют собой "сырые" оценки того, насколько модель уверена в каждом токене. Чем больше логит, тем больше уверенность модели в этом токене.

* T: Это параметр температуры (temperature). Как мы разбирали уже выше, температура используется для "смягчения" распределения вероятностей.

* \exp(x): Это экспоненциальная функцияe^x.

* \sum_j \exp(z_j/T): Это сумма экспоненциальных значений логитов, деленных на температуру, для всех возможных токеновj. Эта сумма используется для нормализации, чтобы вероятности в итоге суммировались к 1.

Пошаговое объяснение:

1. Деление логитов на температуруz_i/T: Когда мы делим логиты на температуруT > 1, мы уменьшаем абсолютные значения логитов.

2. Экспоненцирование\exp(z_i/T): Экспоненциальная функция преобразует логиты в положительные значения.

3. Нормализация\frac{\exp(z_i/T)}{\sum_j \exp(z_j/T)}: Деление на сумму экспоненциальных значений всех логитов гарантирует, что полученные значенияp_i^T будут представлять собой вероятностное распределение, то есть будут неотрицательными и в сумме дадут 1. Это стандартная операция softmax, но с применением температуры.

Интуиция и эффект температуры:

* При высокой температуре (например, T = 2.0), распределение вероятностей становится более "мягким" или "ровным". Вероятности для менее вероятных токенов увеличиваются, а вероятность наиболее вероятного токена уменьшается. Это позволяет "вытащить" больше информации из распределения, включая "темные знания" о менее вероятных, но все же релевантных вариантах.

* При низкой температуре (приближающейся к T = 1.0, или даже меньше), распределение становится более "острым". Вероятность наиболее вероятного токена приближается к 1, а вероятности остальных токенов стремятся к 0. При T=1 это стандартный softmax. ПриT \rightarrow 0 распределение становится дельта-функцией, выбирая только токен с наибольшим логитом.

Figure_1.jpg
Figure_1.jpg

2. Аналогично для студента:

q_i^T = \frac{\exp(z_i^q/T)}{\sum_j \exp(z_j^q/T)}

гдеz_i^q - логит студента для классаi.

Аналогия с формулой учителя: Эта формула абсолютно идентична формуле для учителя, за исключением того, что здесь используются логиты, выданные моделью-студентом.

* q_i^T: "Мягкая" вероятность дляi-го токена, сгенерированная студентом с температуройT.

* z_i^q: Логит дляi-го токена, выданный моделью-студентом.

* Цель: Мы применяем ту же температуруT к распределению студента, чтобы сделать его сопоставимым с "мягкими" метками учителя. Это необходимо для корректного расчета функции потерь дистилляции.

3. Функция потерь для Soft-label Distillation:

L_{soft} = T^2 \cdot \text{KL}(p^T || q^T) = T^2 \cdot \sum_i p_i^T \log\frac{p_i^T}{q_i^T}

МножительT^2 компенсирует уменьшение градиентов из-за temperature scaling.

Разберем компоненты:

* L_{soft}: Функция потерь Soft-label Distillation. Это значение, которое мы хотим минимизировать в процессе обучения студента.

* T^2: Квадрат температуры. Этот множитель используется для масштабирования функции потерь и компенсации уменьшения градиентов, вызванного температурой.

* \text{KL}(p^T || q^T): KL-дивергенция ( Kullback-Leibler divergence) между распределением учителя $p^T$ и распределением студентаq^T.

* \sum_i p_i^T \log\frac{p_i^T}{q_i^T}: Это развернутая формула KL-дивергенции для дискретных распределений.

Пошаговое объяснение KL-дивергенции:

1. \frac{p_i^T}{q_i^T}: Отношение вероятности учителя к вероятности студента для каждого токенаi. Если студент предсказывает вероятностьq_i^T близкую к вероятности учителяp_i^T, это отношение будет близко к 1.

2. \log\frac{p_i^T}{q_i^T}: Логарифм этого отношения. Если отношение близко к 1, логарифм будет близок к 0. Еслиq_i^Tсильно отличается отp_i^T, логарифм будет иметь большее абсолютное значение (отрицательное, еслиq_i^T > p_i^T, и положительное, еслиq_i^T < p_i^T).

3. p_i^T \log\frac{p_i^T}{q_i^T}: Умножение наp_i^T взвешивает вклад каждого токена в общую дивергенцию. Токены, которые учитель считает более вероятными (высокоеp_i^T), вносят больший вклад в функцию потерь.

4. \sum_i p_i^T \log\frac{p_i^T}{q_i^T}: Суммирование по всем токенамi дает общую KL-дивергенцию. KL-дивергенция измеряет "расстояние" между двумя распределениями вероятностей. В контексте дистилляции, она измеряет, насколько распределение студентаq^T отличается от распределения учителяp^T.

РольT^2:

* Применение температурыT "смягчает" распределения, что может привести к уменьшению величины градиентов при обучении. Умножение наT^2 масштабирует функцию потерь, чтобы компенсировать это уменьшение и сделать градиенты более значимыми, особенно на ранних этапах обучения. Это эмпирическая коррекция, которая помогает стабилизировать и ускорить обучение.

* ЦельL_{soft}: МинимизируяL_{soft}, мы заставляем распределение вероятностей студентаq^T максимально приблизиться к распределению вероятностей учителяp^T. Студент учится не только предсказывать "правильный" токен, но и имитировать всю "манеру мышления" учителя, выраженную в распределении вероятностей.

4. Комбинированная функция потерь:

L = \alpha \cdot L_{soft} + (1-\alpha) \cdot L_{hard}

гдеL_{hard} - стандартная кросс-энтропия с истинными метками,\alpha - коэффициент баланса.

Разберем компоненты:

* L: Общая функция потерь, используемая для обучения студента.

* \alpha: Коэффициент баланса (обычно от 0.5 до 0.9). Он определяет, насколько сильно мы полагаемся на "мягкие" метки учителя по сравнению со стандартными "жесткими" метками.

* L_{soft}: Функция потерь Soft-label Distillation, которую мы разобрали выше.

* L_{hard}: Стандартная функция потерь "жестких" меток, обычно кросс-энтропия между предсказаниями студента и истинными (one-hot) метками.


L_{hard} (Стандартные потери "жестких" меток):

* В обычной задаче обучения языковой модели, мы имеем "жесткие" метки - это истинные следующие токены в обучающих данных. Например, для фразы "Столица Франции - это Париж", "Париж" является "жесткой" меткой.

* L_{hard} вычисляется как кросс-энтропия между распределением вероятностей, предсказанным студентом (обычно сT=1, то есть стандартный softmax), и one-hot вектором, представляющим истинный токен. Эта функция потерь заставляет студента предсказывать именно "правильный" токен.

КомбинированиеL_{soft} иL_{hard}:

* Комбинирование "мягких" и "жестких" потерь позволяет студенту учиться как у учителя (черезL_{soft}), так и из исходных данных (черезL_{hard}).

* Коэффициент\alpha позволяет настроить баланс.

* Высокое\alpha (например, 0.9) означает, что мы больше полагаемся на знания учителя, переданные через "мягкие" метки. Это может быть полезно, когда учитель обладает значительно лучшими знаниями, чем можно извлечь только из "жестких" меток.

* Низкое\alpha (например, 0.5) означает, что мы в равной степени учитываем как знания учителя, так и "жесткие" метки. Это может быть полезно, когда мы хотим, чтобы студент сохранил способность хорошо работать и на исходных данных, а не только имитировал учителя.

Практическая реализация Soft-label Distillation для GPT моделей

Программный код был заимствован из репозитория: https://github.com/arcee-ai/DistillKit

1. Конфигурация дистилляции

Первым шагом необходимо настроить параметры дистилляции, включая температуру и коэффициент баланса между мягкими и жесткими метками:

"""
Здесь temperature: 2.0 соответствует параметру T в формулах, который "смягчает" распределение вероятностей, а alpha: 0.5 - это коэффициент α, который определяет соотношение между потерями от мягких и жестких меток.
"""

config = {
    "project_name": "distil-multilayer",    # Название проекта
    "dataset": {
        "name": "mlabonne/FineTome-100k",   # Название датасета
        "split": "train",                   # Раздел датасета для тренировки
        "num_samples": 1000,                # Количество образцов для тренировки (можно ограничить)
        "seed": 42                          # Значение для инициализации генератора случайных чисел
    },
    "models": {
        "teacher": "arcee-ai/Arcee-Spark",  # Модель учителя
        "student": "Qwen/Qwen2-1.5B"        # Модель студента
    },
    "tokenizer": {
        "max_length": 4096,                 # Максимальная длина токенов
        "chat_template": (
            "{% for message in messages %}"
            "{% if loop.first and messages[0]['role'] != 'system' %}"
            "{{ '<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n' }}"
            "{% endif %}"
            "{{'<|im_start|>' + message['role'] + '\n' + message['content'] + '<|im_end|>' + '\n'}}"
            "{% endfor %}"
            "{% if add_generation_prompt %}"
            "{{ '<|im_start|>assistant\n' }}"
            "{% endif %}"
        )                                    # Шаблон для форматирования сообщений в чате
    },
    "training": {
        "output_dir": "./results",           # Директория для сохранения результатов
        "num_train_epochs": 3,               # Количество эпох для тренировки
        "per_device_train_batch_size": 1,    # Размер батча для тренировки на одном устройстве
        "gradient_accumulation_steps": 8,    # Количество шагов для накопления градиентов
        "save_steps": 1000,                  # Шаги для сохранения модели
        "logging_steps": 2,                  # Шаги для логирования
        "save_total_limit": 2,               # Лимит на количество сохраняемых моделей
        "learning_rate": 2e-5,               # Скорость обучения
        "weight_decay": 0.01,                # Коэффициент регуляризации
        "warmup_ratio": 0.2,                 # Доля шагов для разгона скорости обучения
        "lr_scheduler_type": "linear",       # Тип планировщика скорости обучения
        "resume_from_checkpoint": None,      # Путь к чекпоинту для возобновления тренировки (если есть)
        "fp16": False,                       # Использовать ли 16-битное число с плавающей точкой
        "bf16": True,                        # Использовать ли BFloat16
        "max_grad_norm": 1.0,                # Максимальная норма градиента
        "group_by_length": False             # Группировать ли батчи по длине
    },
    "distillation": {
        "temperature": 2.0,                  # Температура для дистилляции
        "alpha": 0.5                         # Коэффициент альфа для дистилляции
    },
    "model_config": {
        "use_flash_attention": True          # Использовать ли Flash Attention
    }
}

2. Подготовка моделей учителя и студента

Для дистилляции необходимо загрузить как модель-учитель (более крупную), так и модель-студент (более компактную):

import torch
from typing import Dict, Any
from transformers import AutoModelForCausalLM

def load_models_with_flash_attention(config: Dict[str, Any]) -> Dict[str, AutoModelForCausalLM]:
    """
    Description:
    ---------------
        Загружает модели с настройкой флеш-внимания для ускорения.

    Args:
    ---------------
        config: Конфигурация моделей и параметров

    Returns:
    ---------------
        Словарь с загруженными моделями

    Raises:
    ---------------
        KeyError: Если в конфигурации отсутствуют необходимые ключи

    Examples:
    ---------------
        >>> config = {
        ...     "model_config": {"use_flash_attention": True},
        ...     "models": {"teacher": "teacher_model_path", "student": "student_model_path"}
        ... }
        >>> load_models_with_flash_attention(config)
        {'teacher_model': <transformers.models.model_name.model.ModelName object>,
         'student_model': <transformers.models.model_name.model.ModelName object>}
    """
    # Настройки для загрузки моделей
    model_kwargs: Dict[str, Any] = {"torch_dtype": torch.bfloat16}

    # Проверка на использование flash attention
    if config["model_config"]["use_flash_attention"]:
        model_kwargs["attn_implementation"] = "flash_attention_2"

    # Загрузка моделей
    teacher_model = AutoModelForCausalLM.from_pretrained(config["models"]["teacher"], **model_kwargs)
    student_model = AutoModelForCausalLM.from_pretrained(config["models"]["student"], **model_kwargs)

    return {"teacher_model": teacher_model, "student_model": student_model}

# Вызов функции
models = load_models_with_flash_attention(config)

# Теперь models содержит загруженные модели
teacher_model = models["teacher_model"]
student_model = models["student_model"]

3. Реализация функции потерь с мягкими метками

Ключевым компонентом является функция потерь Soft-label Distillation. Рассмотрим её реализацию из файла distil_logits.py:

"""
Это прямая реализация формулы KL-дивергенции. Обратите внимание на следующие ключевые моменты:

1. Логиты масштабируются температурой T перед применением функций softmax/log_softmax.
2. Потери умножаются на T² для компенсации уменьшения градиентов, как описано в теории.
3. Финальная функция потерь комбинирует мягкие метки (KL-дивергенция) и жесткие метки (original_loss) с коэффициентом α.
"""

from typing import Any
import torch
import torch.nn.functional as F

def distillation_loss(
    self,
    student_logits: torch.Tensor,
    teacher_logits: torch.Tensor,
    inputs: Any,
    original_loss: torch.Tensor,
    config: Dict[str, Any]
) -> torch.Tensor:
    """
    Description:
    ---------------
        Вычисляет потери дистилляции между логитами студента и учителя.

    Args:
    ---------------
        student_logits: Логиты студента.
        teacher_logits: Логиты учителя.
        inputs: Входные данные.
        original_loss: Исходные потери.
        config: Конфигурация моделей и параметров.

    Returns:
    ---------------
        Общие потери, включающие дистилляционные потери и исходные потери.

    Raises:
    ---------------
        KeyError: Если в конфигурации отсутствуют необходимые ключи.

    Examples:
    ---------------
        >>> config = {
        ...     "distillation": {"temperature": 2.0, "alpha": 0.5},
        ...     "tokenizer": {"max_length": 512}
        ... }
        >>> student_logits = torch.randn(3, 512)
        >>> teacher_logits = torch.randn(3, 512)
        >>> inputs = ...
        >>> original_loss = torch.tensor(0.5)
        >>> distillation_loss(self, student_logits, teacher_logits, inputs, original_loss, config)
        tensor(0.25)
    """
    # Приведение размерностей логитов учителя и студента к одинаковому размеру
    student_logits, teacher_logits = pad_logits(
        student_logits.to(self.model.device),
        teacher_logits.to(self.model.device)
    )

    # Масштабирование логитов с помощью температуры T
    temperature = config["distillation"]["temperature"]
    student_logits_scaled = student_logits / temperature
    teacher_logits_scaled = teacher_logits / temperature

    # Расчёт KL-дивергенции между распределениями учителя и студента
    loss_kd = F.kl_div(
        F.log_softmax(student_logits_scaled, dim=-1),  # log(q_i^T)
        F.softmax(teacher_logits_scaled, dim=-1),      # p_i^T
        reduction='batchmean'
    ) * (temperature ** 2) / config["tokenizer"]["max_length"]

    # Комбинирование потерь от мягких и жестких меток
    alpha = config["distillation"]["alpha"]
    total_loss = alpha * loss_kd + (1 - alpha) * original_loss

    return total_loss

4. Обработка различных размеров словарей

Поскольку модели учителя и студента могут иметь разный размер словаря токенов, необходима дополнительная функция для согласования размерности их логитов:

"""
Эта функция добавляет нулевые логиты к меньшему распределению, чтобы обеспечить одинаковую размерность для сравнения распределений.
"""

from typing import Tuple
import torch

def pad_logits(
    student_logits: torch.Tensor,
    teacher_logits: torch.Tensor
) -> Tuple[torch.Tensor, torch.Tensor]:
    """
    Description:
    ---------------
        Приводит размерности логитов студента и учителя к одинаковому размеру.

    Args:
    ---------------
        student_logits: Логиты студента.
        teacher_logits: Логиты учителя.

    Returns:
    ---------------
        Кортеж из логитов студента и учителя с одинаковыми размерностями.

    Raises:
    ---------------
        ValueError: Если размерности логитов не совпадают и не могут быть приведены к одинаковому размеру.

    Examples:
    ---------------
        >>> student_logits = torch.randn(3, 512)
        >>> teacher_logits = torch.randn(3, 510)
        >>> pad_logits(student_logits, teacher_logits)
        (tensor([...]), tensor([...]))
    """
    # Определение размеров логитов
    student_size, teacher_size = student_logits.size(-1), teacher_logits.size(-1)

    # Если размеры не совпадают, добавляем паддинг
    if student_size != teacher_size:
        pad_size = abs(student_size - teacher_size)
        pad_tensor = torch.zeros(
            (*teacher_logits.shape[:-1], pad_size),
            dtype=teacher_logits.dtype,
            device=teacher_logits.device
        )

        # Возвращаем логиты с добавленным паддингом
        if student_size < teacher_size:
            return torch.cat([student_logits, pad_tensor], dim=-1), teacher_logits
        else:
            return student_logits, torch.cat([teacher_logits, pad_tensor], dim=-1)

    # Возвращаем логиты без изменений, если размеры совпадают
    return student_logits, teacher_logits

5. Кастомный тренер для дистилляции

Для интеграции процесса дистилляции в процесс обучения создаётся специальный класс тренера, который переопределяет функцию вычисления потерь:

"""
Этот класс:
1. Получает выходы (логиты) как от студента, так и от учителя
2. Замораживает веса учителя с помощью `torch.no_grad()`
3. Вычисляет комбинированную функцию потерь с использованием потерь от мягких и жестких меток
"""

from typing import Dict, Any, Union, Tuple
import torch
import torch.nn.functional as F
from transformers import SFTTrainer

class LogitsTrainer(SFTTrainer):
    """
    Description:
    ---------------
        Класс для обучения модели с использованием дистилляции логитов.
    """

    def compute_loss(
        self,
        model: torch.nn.Module,
        inputs: Dict[str, Any],
        return_outputs: bool = False
    ) -> Union[torch.Tensor, Tuple[torch.Tensor, Any]]:
        """
        Description:
        ---------------
            Вычисляет комбинированную функцию потерь для модели студента и учителя.

        Args:
        ---------------
            model: Модель студента.
            inputs: Входные данные.
            return_outputs: Флаг для возврата выходов модели.

        Returns:
        ---------------
            Комбинированная функция потерь и, если указано, выходы модели.

        Raises:
        ---------------
            ValueError: Если входные данные не соответствуют ожидаемым.

        Examples:
        ---------------
            >>> model = ...
            >>> inputs = ...
            >>> trainer = LogitsTrainer()
            >>> trainer.compute_loss(model, inputs, return_outputs=True)
            (tensor(0.5), ...)
        """
        # Перемещение входных данных на устройство модели
        inputs = {k: v.to(model.device) if hasattr(v, 'to') else v for k, v in inputs.items()}

        # Перемещение модели учителя на устройство модели
        self.teacher_model = self.teacher_model.to(model.device)

        # Получение модулей моделей, если они существуют
        student_model = model.module if hasattr(model, 'module') else model
        teacher_model = self.teacher_model.module if hasattr(self.teacher_model, 'module') else self.teacher_model

        # Получение выходов моделей
        student_outputs = student_model(**inputs)
        with torch.no_grad():  # Учитель не обучается
            teacher_outputs = teacher_model(**inputs)

        # Вычисление комбинированной функции потерь
        custom_loss = self.distillation_loss(
            student_outputs.logits,
            teacher_outputs.logits,
            inputs,
            student_outputs.loss
        )

        # Возврат потерь и выходов модели, если указано
        if return_outputs:
            return custom_loss, student_outputs
        return custom_loss

    def pad_logits(
        self,
        student_logits: torch.Tensor,
        teacher_logits: torch.Tensor
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """
        Description:
        ---------------
            Приводит размерности логитов студента и учителя к одинаковому размеру.

        Args:
        ---------------
            student_logits: Логиты студента.
            teacher_logits: Логиты учителя.

        Returns:
        ---------------
            Кортеж из логитов студента и учителя с одинаковыми размерностями.

        Raises:
        ---------------
            ValueError: Если размерности логитов не совпадают и не могут быть приведены к одинаковому размеру.

        Examples:
        ---------------
            >>> student_logits = torch.randn(3, 512)
            >>> teacher_logits = torch.randn(3, 510)
            >>> trainer = LogitsTrainer()
            >>> trainer.pad_logits(student_logits, teacher_logits)
            (tensor([...]), tensor([...]))
        """
        # Определение размеров логитов
        student_size, teacher_size = student_logits.size(-1), teacher_logits.size(-1)

        # Если размеры не совпадают, добавляем паддинг
        if student_size != teacher_size:
            pad_size = abs(student_size - teacher_size)
            pad_tensor = torch.zeros(
                (*teacher_logits.shape[:-1], pad_size),
                dtype=teacher_logits.dtype,
                device=teacher_logits.device
            )

            # Возвращаем логиты с добавленным паддингом
            if student_size < teacher_size:
                return torch.cat([student_logits, pad_tensor], dim=-1), teacher_logits
            else:
                return student_logits, torch.cat([teacher_logits, pad_tensor], dim=-1)

        # Возвращаем логиты без изменений, если размеры совпадают
        return student_logits, teacher_logits

    def distillation_loss(
        self,
        student_logits: torch.Tensor,
        teacher_logits: torch.Tensor,
        inputs: Any,
        original_loss: torch.Tensor
    ) -> torch.Tensor:
        """
        Description:
        ---------------
            Вычисляет потери дистилляции между логитами студента и учителя.

        Args:
        ---------------
            student_logits: Логиты студента.
            teacher_logits: Логиты учителя.
            inputs: Входные данные.
            original_loss: Исходные потери.

        Returns:
        ---------------
            Общие потери, включающие дистилляционные потери и исходные потери.

        Raises:
        ---------------
            KeyError: Если в конфигурации отсутствуют необходимые ключи.

        Examples:
        ---------------
            >>> config = {
            ...     "distillation": {"temperature": 2.0, "alpha": 0.5},
            ...     "tokenizer": {"max_length": 512}
            ... }
            >>> student_logits = torch.randn(3, 512)
            >>> teacher_logits = torch.randn(3, 512)
            >>> inputs = ...
            >>> original_loss = torch.tensor(0.5)
            >>> trainer = LogitsTrainer()
            >>> trainer.distillation_loss(student_logits, teacher_logits, inputs, original_loss)
            tensor(0.25)
        """
        # Приведение размерностей логитов учителя и студента к одинаковому размеру
        student_logits, teacher_logits = self.pad_logits(
            student_logits.to(self.model.device),
            teacher_logits.to(self.model.device)
        )

        # Масштабирование логитов с помощью температуры T
        temperature = config["distillation"]["temperature"]
        student_logits_scaled = student_logits / temperature
        teacher_logits_scaled = teacher_logits / temperature

        # Расчёт KL-дивергенции между распределениями учителя и студента
        loss_kd = F.kl_div(
            F.log_softmax(student_logits_scaled, dim=-1),  # log(q_i^T)
            F.softmax(teacher_logits_scaled, dim=-1),      # p_i^T
            reduction='batchmean'
        ) * (temperature ** 2) / config["tokenizer"]["max_length"]

        # Комбинирование потерь от мягких и жестких меток
        alpha = config["distillation"]["alpha"]
        total_loss = alpha * loss_kd + (1 - alpha) * original_loss

        return total_loss

6. Подготовка тренера и запуск обучения

После определения всех компонентов можно инициализировать тренер и запустить процесс дистилляции:

"""
Обратите внимание, что модель-учитель добавляется к тренеру как атрибут, чтобы она была доступна внутри функции `compute_loss`.
"""

# Импорт необходимых библиотек
from transformers import TrainingArguments
from accelerate import Accelerator

# Инициализация accelerator
accelerator = Accelerator()

# Аргументы обучения
training_arguments = TrainingArguments(**config["training"])

# Проверка наличия предобработанного датасета
if 'tokenized_dataset' not in locals():
    # Если датасет не предобработан, выполняем необходимую предобработку
    # Код предобработки датасета должен быть здесь...
    print("Необходимо сначала выполнить предобработку датасета!")

# Создание кастомного SFT тренера
trainer = LogitsTrainer(
    model=student_model,
    train_dataset=tokenized_dataset["train"],
    eval_dataset=tokenized_dataset["test"],
    tokenizer=student_tokenizer,
    args=training_arguments,
    max_seq_length=config["tokenizer"]["max_length"],
    dataset_text_field="text",
)

# Добавление модели-учителя к тренеру
trainer.teacher_model = teacher_model

# Подготовка к распределенному обучению
trainer = accelerator.prepare(trainer)

# Запуск обучения
trainer.train(resume_from_checkpoint=config["training"]["resume_from_checkpoint"])

# Сохранение финальной модели
trainer.save_model(config["training"]["output_dir"])

print(f"Обучение завершено. Модель сохранена в {config['training']['output_dir']}")

Преимущества Soft-label Distillation:

  • Более полная передача знаний: Студент получает доступ к "темным знаниям" учителя — информации о сложных случаях, тонких различиях между классами и степени неопределенности.

  • Лучшие результаты: Студенты, обученные этим методом, обычно демонстрируют производительность ближе к учителю по сравнению с Hard-label Distillation.

  • Улучшенная генерализация: Модели лучше работают на новых данных, так как учатся не только "что" предсказывать, но и "с какой уверенностью".

  • Контроль через температуру: Параметр T позволяет настраивать степень "мягкости" дистилляции. Более высокие значения T делают распределение более равномерным, помогая передать больше информации о маловероятных классах.

  • Совместимость с другими методами: Легко комбинируется с другими техниками улучшения моделей.

Недостатки Soft-label Distillation:

  • Вычислительные затраты: Для языковых моделей с большими словарями (50,000+ токенов) хранение и передача полных распределений вероятностей требует значительных ресурсов.

  • Сложность реализации: Требует доступа к логитам/вероятностям учителя, а не только к финальным предсказаниям.

  • Настройка гиперпараметров: Необходимо тщательно подбирать температуру T и коэффициент α для оптимальных результатов.

  • Зависимость от качества учителя: Если учитель имеет систематические ошибки, они могут передаться студенту.

Сравнение Hard-label и Soft-label Distillation:

Аспект

Hard-label Distillation

Soft-label Distillation

Передаваемая информация

Только итоговые классы/токены

Полные распределения вероятностей

Температура

Не используется

Используется для "смягчения" распределений

Сложность реализации

Простая

Средняя

Вычислительные требования

Низкие

Средние-высокие

Объем хранимых данных

Малый

Большой (особенно для языковых моделей)

Качество получаемой модели

Хорошее

Лучшее

Способность передавать неопределенность

Низкая

Высокая

Эффективность для языковых моделей

Средняя

Высокая

В заключение, Soft-label Distillation предлагает более мощный метод передачи знаний от учителя к ученику, особенно для сложных задач, где важны тонкие различия между классами и понимание неопределенности. Ключевое отличие от Hard-label Distillation заключается в использовании полных распределений вероятностей и temperature scaling, что позволяет извлечь "темные знания" и научить студента не только выдавать правильные ответы, но и воспроизводить тонкие нюансы рассуждений учителя.

Part 2: Законы масштабирования дистилляции

После того, как DeepSeek представил в open source свой метод дистилляции знаний для R1, исследователи из Apple и Оксфордского университета быстро предложили закон масштабирования дистилляции и уже 28 февраля завершили все эксперименты и загрузили 67-страничную статью на arXiv.

Рассмотрим мотивацию исследования, которая сводится к следующим пунктам:

  1. Текущее состояние исследований законов масштабирования моделей: В последние годы исследования выявили взаимосвязь между производительностью языковых моделей, их размером и объемом данных для обучения. Однако систематических исследований законов масштабирования в контексте дистилляции пока не проводилось.

  2. Проблема стоимости вывода модели: С увеличением размера языковых моделей значительно возрастает стоимость вывода. Исследование того, как снизить стоимость вывода без потери производительности, становится важной задачей.

  3. Эффективность и производительность дистилляции: Теоретически, дистилляция может снизить стоимость вывода, однако в академических кругах нет единого мнения относительно методов дистилляции, особенно в том, как рационально распределить вычислительные ресурсы для создания наиболее мощных моделей, что остается большой неопределенностью.

Экстраполяция закона масштабирования дистилляции
Экстраполяция закона масштабирования дистилляции

Экстраполяции закона масштабирования дистилляции. Закон масштабирования дистилляции (Уравнение 8) аппроксимирован на слабых учениках L_S > 2.3 для ряда учителей с потерямиL_T. Сплошные линии представляют прогнозируемое поведение модели для невидимых учителей при заданной конфигурации ученика (интерполяция), а пунктирные линии представляют прогнозируемое поведение модели за пределами видимых учителей и для области сильных учеников ( L_S \leq 2.3 ).

Закон масштабирования дистилляции

Традиционный закон масштабирования (Scaling Laws) для больших моделей демонстрирует, что производительность языковой модели (LM) может улучшаться с увеличением вычислительных ресурсов, если модель следует оптимальной вычислительной парадигме обучения. Однако постоянный рост затрат на инференс делает этот подход все менее практичным, что заставляет исследователей искать альтернативные методы, включая переобучение и дистилляцию, для создания небольших, но мощных моделей.

Исследователи провели обширные эксперименты, используя модели-студенты и модели-учителя с параметрами от 143 миллионов до 12,6 миллиардов и объемом данных до 512 миллиардов токенов. Целью было изучить взаимосвязь между производительностью модели и вычислительными ресурсами в процессе дистилляции, а также найти способы оптимизации распределения этих ресурсов.

В следующей таблице показано значение символов, используемых в этой статье:

Таблица. Выражения, связанные с законами масштабирования, используемые в данной работе. В каждом случаеS всегда относится к ученику, а не к обучению с учителем.

Выражение

Значение

N / N_S / N_T

Количество параметров модели/ученика/учителя, не связанных с эмбеддингом. В тексте, когда мы упоминаем параметры, мы всегда имеем в виду параметры, не связанные с эмбеддингом, если не указано иное. Подробности см. в Приложении H.2.

D / D_T

Количество токенов, на которых предобучена модель/учитель.

D_S

Количество токенов, на которых дистиллирован ученик.

M \equiv D / N

Соотношение токенов на параметр, или MM-соотношение. В работе Hoffmann et al. (2022), M принимает оптимальное значение M^∗≈20, что является эмпирическим правилом Chinchilla.

L \approx L(N, D)

Кросс-энтропия модели, которая представляет собой валидационную кросс-энтропию модели на данных, оцениваемую по закону масштабирования с учителем для модели с N параметрами, обученной на D токенах. (Уравнение 1).

L_T \approx L(N_T, D_T)

Кросс-энтропия учителя, которая представляет собой валидационную кросс-энтропию учителя на данных, оцениваемую по закону масштабирования с учителем для учителя с N_T​ параметрами, обученного на D_T​ токенах.

L_S \approx L_S(N_S, D_S, L_T)

Кросс-энтропия ученика, которая представляет собой валидационную кросс-энтропию ученика на данных, оцениваемую по нашему закону масштабирования дистилляции для ученика с N_S​ параметрами, дистиллированного на D_S​ токенах с использованием учителя с потерей предобучения L_T​ (Уравнение 8).

\tilde{L}_S \approx L(N_S, D_S)

Кросс-энтропия ученика с учителем, которая представляет собой валидационную кросс-энтропию ученика на данных, если бы ученик был обучен с учителем, оцениваемую по закону масштабирования с учителем для ученика с N_S​ параметрами, обученного наD_S​ токенах.

Пояснение: Кросс-энтропия — это метрика, измеряющая расхождение между предсказанным распределением вероятностей модели и истинным распределением. Чем ниже кросс-энтропия, тем лучше модель предсказывает правильные токены. Это основной показатель качества языковой модели.

Пояснение к правилу Чинчиллы: Исследование Hoffmann et al. (2022) установило эмпирическое правило оптимального соотношения между количеством параметров модели и количеством токенов для обучения — примерно 20 токенов на каждый параметр. Это правило позволяет эффективно распределять вычислительные ресурсы при обучении крупных языковых моделей.

Формализация закона масштабирования дистилляции

Центральным вкладом исследования является формулировка закона масштабирования дистилляции:

L_S(N_S, D_S, L_T) = L_T + \frac{1}{L_{c_0}^T} \left( 1 + \left( \frac{L_T}{\tilde{L}_S^{d_1}} \right)^{1/f_1} \right)^{-c_1f_1} \left( \frac{A}{N_S^{\alpha'}} + \frac{B}{D_S^{\beta'}} \right)^{\gamma'}

Объяснение переменных:

L_S(N_S, D_S, L_T) — кросс-энтропия студента (мера ошибки предсказания; чем ниже, тем лучше модель).

L_T — кросс-энтропия учителя (мера ошибки предсказания большой модели).

N_S — количество неэмбеддинговых параметров студента (основные обучаемые параметры модели).

D_S — количество токенов, использованных для обучения студента при дистилляции.

\tilde{L}_S = L(N_S, D_S) — потенциальная кросс-энтропия студента при обычном обучении без дистилляции, определяемая классическим законом масштабирования:

L(N, D) = E - \frac{A}{N^\alpha} - \frac{B}{D^\beta}

\{c_0, c_1, d_1, f_1, \alpha', \beta', \gamma'\} — коэффициенты, определяемые эмпирически.

A иB — положительные коэффициенты, зависящие от архитектуры модели и характеристик набора данных.

Физический смысл формулы:

1. Базовая часть:L_T — студент не может быть лучше учителя.

2. Модифицирующая часть: Остальная часть формулы описывает, насколько эффективно студент может приблизиться к учителю в зависимости от своего размера, количества данных и качества учителя.

Ключевые выводы:

1. Студент не может превзойти учителя (всегдаL_S \geq L_T). Кросс-энтропия (L) - это мера ошибки модели. Чем ниже значение L, тем лучше модель предсказывает данные.

2. Чем ближе потенциальная производительность студента к производительности учителя, тем эффективнее дистилляция.

3. При фиксированном учителе закон масштабирования дистилляции не превосходит обычный закон масштабирования.

Практическое применение:

Этот закон позволяет оптимально распределить вычислительные ресурсы между учителем и студентом и прогнозировать эффективность дистилляции.

То есть: Этот закон описывает, как качество маленькой модели зависит от трех факторов: размера самой модели, количества данных для обучения и качества большой модели-учителя. Ключевой вывод: студент никогда не может быть лучше учителя, но насколько близко он подойдет к учителю, зависит от его собственных возможностей и объема тренировки.

Коэффициенты смешивания в процессе дистилляции знаний

Рассмотрев общий закон масштабирования дистилляции, важно также понять практические аспекты реализации этого процесса, в частности, как управлять балансом между имитацией учителя и самостоятельным обучением модели-ученика.

Основная идея дистилляции знаний заключается в переносе информации от большой модели-учителя к компактной модели-ученику. В этом процессе прогнозируемое распределение вероятностей модели-учителя используется в качестве целевого распределения для модели-ученика. Обучение происходит путем минимизации расхождения Кульбака-Лейблера (KL-дивергенции) между распределениями ученика и учителя:

{L}_{\text{KD}} \left( z_T^{(i)}, z_S^{(i)} \right) = -\tau^2 \sum_{a=1}^V \sigma_a \left( \frac{z_T^{(i)}}{\tau} \right) \log \sigma_a \left( \frac{z_S^{(i)}}{\tau} \right)

где:

-z_T^{(i)} иz_S^{(i)} — выходные логиты моделей учителя и ученика соответственно

-\tau — температура дистилляции, контролирующая "сглаженность" распределения вероятностей учителя

-\sigma_a — функция softmax, преобразующая логиты в вероятности

-V — размер словаря

Комбинированная функция потерь для модели-ученика объединяет несколько компонентов:

{L}_S\big(x^{(i)}, \boldsymbol{z}_T^{(i)},\boldsymbol{z}_S^{(i)}\big) = (1-\lambda)\,{L}_{\textrm{NTP}}(x^{(i)},\boldsymbol{z}_S^{(i)}) + \lambda\,{L}_{\textrm{KD}}(\boldsymbol{z}_T^{(i)},\boldsymbol{z}_S^{(i)}) + \lambda_Z\,{L}_Z(\boldsymbol{z}_S^{(i)})

где:

-{L}_{\textrm{NTP}} — потеря при предсказании следующего токена (стандартная кросс-энтропия)

-{L}_{\textrm{KD}}— потеря при дистилляции знаний (KL-дивергенция)

-{L}_Z— регуляризационная Z-потеря, стабилизирующая обучение путем нормализации логитов

-\lambda— коэффициент смешивания, определяющий баланс между обучением на "чистых" данных и имитацией учителя

-\lambda_Z— весовой коэффициент для Z-потери

Экспериментальное определение оптимальных параметров дистилляции

Для определения влияния параметров дистилляции на эффективность закона масштабирования, исследователи провели серию экспериментов. Чтобы исключить влияние данных и сосредоточиться именно на роли модели-учителя, эксперименты проводились в режиме "чистой дистилляции" с λ=1. Результаты показали, что такой выбор λ даёт результаты, статистически сопоставимые с использованием оптимальных значений λ^∗.

Во всех экспериментах использовалась фиксированная температура дистилляции τ=1, которая эмпирически показала наилучшую эффективность для обучения модели-ученика.

Коэффициенты смешивания λ
Коэффициенты смешивания λ

Коэффициенты смешивания\lambda.

(a) Модели-ученики шести размеровN_S \in \{198M, 266M, \ldots, 2.72B\}, обученные с соотношением M = D_S/N_S = 20, дистиллируются от моделей-учителей размеров N_T \in \{546M, 975M, \ldots, 7.75B\}, обученных с соотношениеM = D_T/N_T = 20, с различными значениями коэффициента смешивания \lambda \in [0, 1]. Значения\lambda = 0 и\lambda = 1 соответствуют стандартному обучению и чистой дистилляции соответственно.

(b) Оптимальные коэффициенты смешивания\lambda^* = \arg \min_{\lambda} {L}(\lambda), дающие наименьшую потерю на валидационном наборе для каждой пары учитель-ученик.

Эти эксперименты подтверждают, что параметры дистилляции оказывают существенное влияние на итоговую производительность модели-ученика, и их оптимальный выбор напрямую связан с размерами моделей учителя и ученика, что согласуется с общим законом масштабирования дистилляции.

Вывод

Дистилляция знаний — это метод, позволяющий передать способности большой нейронной модели (учителя) меньшей и вычислительно эффективной модели (ученику). Процесс основан на обучении модели-ученика имитировать распределение вероятностей модели-учителя путём минимизации расхождения Кульбака-Лейблера между их предсказаниями.

Эффективность дистилляции определяется балансом нескольких компонентов в функции потерь:

  • Стандартной кросс-энтропии при предсказании следующего токена

  • KL-дивергенции при имитации учителя

  • Регуляризационной Z-потери для стабилизации обучения

Два ключевых параметра контролируют этот процесс:

  • Коэффициент смешивания λ, регулирующий баланс между самостоятельным обучением и имитацией учителя

  • Температура дистилляции τ, влияющая на "сглаженность" распределения вероятностей

Экспериментальные исследования демонстрируют, что режим "чистой дистилляции" (λ = 1) при температуре τ = 1 часто даёт результаты, сопоставимые с оптимально подобранными параметрами. Однако наиболее важным открытием является то, что идеальные значения этих параметров системно зависят от соотношения размеров конкретной пары моделей учитель-ученик.

Это открытие соответствует общему закону масштабирования дистилляции и имеет прямое практическое применение: для достижения максимальной эффективности при практической реализации дистилляции необходим индивидуальный подбор параметров с учётом размеров используемых моделей, что позволяет существенно улучшить итоговую производительность компактной модели при сохранении её вычислительной эффективности.

Эксперимент с фиксированным учитилем и разными учениками

Размер модели учителя и объем обучающих данных на которых обучался учитель, фиксированы, а размер модели ученика и объем дистилляционных данных варьируются. Цель состоит в том, чтобы изучить, как производительность модели ученика меняется в зависимости от ее размера и объема обработанных дистилляционных данных в условиях фиксированной модели учителя. Таким образом, можно определить оптимальную производительность модели студента при различных масштабах и объемах данных.

Figure_5
Figure_5
Figure_6
Figure_6

Из результатов эксперимента можно заметить, что:

  • При высокой вычислительной мощности, чем больше масштаб параметров модели ученика, тем меньше его функция потерь, и чем больше масштаб модели учителя, тем очевиднее эта тенденция.

  • Когда размер моделей ученика и учителя определен, становится понятно, что чем больше вычислительная мощность, тем лучше будет работать модель ученика.

  • При низкой вычислительной мощности производительность модели сначала улучшится, а затем ослабнет с размером модели. Здесь легко понять, что более крупные модели не полностью обучаются при меньшей вычислительной мощности.

  • В особых случаях модель ученика может превзойти модель учителя и показать способность к обобщению. Я лично предполагаю, что модель учителя может быть недообучена в таких сценариях.

Эксперимент с фиксированным учеником и разными учителями

Размер модели ученика и объем данных дистилляции фиксированы, а размер модели учителя и объем обучающих данных варьируются. Цель состоит в том, чтобы изучить, как эффективность модели учителя влияет на конечную эффективность модели ученика. Таким образом, можно определить оптимальный размер модели учителя и объем обучающих данных для максимизации производительности модели ученика.

Figure_7
Figure_7

Как видно из результатов, чем больше параметры у модели учителя, тем ниже перекрестная энтропия модели ученика. Это показывает, что для достижения наилучшего эффекта дистилляции производительность модели учителя должна соответствовать возможностям модели ученика.

Дистилляция против контролируемого обучения

Чтобы понять, когда дистилляция приносит пользу, на следующем рисунке сравнивается производительность дистилляции и контролируемого обучения при фиксированных вычислительных ресурсах. Результаты показывают, что контролируемое обучение всегда превосходит дистилляцию при наличии достаточного количества вычислений или данных у учащихся. При умеренном бюджете данных дистилляция имеет преимущества, однако при наличии больших объемов данных контролируемое обучение превосходит дистилляцию.

Подводя итог, можно сказать, что при ограниченных вычислительных ресурсах дистилляция обычно более эффективна, чем контролируемое обучение. Это связано с тем, что дистилляция может быстрее усваивать эффективные представления признаков под руководством модели учителя, тем самым достигая более высокой производительности при меньших вычислительных ресурсах.

Figure_8
Figure_8

Выбор модели учителя

  • Сила обучающего сигнала: Модели учителей разных размеров могут обеспечивать разную силу обучающего сигнала, которая обычно измеряется с помощью потери перекрестной энтропии. Более крупная модель учителя может обеспечить более сильный сигнал обучения (более низкая перекрестная энтропия), тем самым помогая модели ученика лучше учиться.

  • Увеличение затрат: использование более крупной модели учителя повлечет за собой более высокие затраты из-за необходимости вычисления логитов модели учителя. Это означает, что более крупная модель учителя не только более затратна в обучении, но и потребляет больше вычислительных ресурсов при использовании для дистилляции.

На рисунке ниже показано изменение потери перекрестной энтропии модели студента при различных бюджетах данных дистилляции. Результаты показывают, что оптимальная потеря учителя (представленная красной линией) уменьшается по степенному закону с увеличением численности учащихся до тех пор, пока потеря ученика не сравняется с оптимальной потерей учителя.

Figure_9
Figure_9

Как видно на другом рисунке ниже, по мере увеличения объема данных дистилляции, перекрестная энтропия оптимальной модели учителя постепенно уменьшается. Таким образом, можно сделать вывод, что: когда вычислительные ресурсы ограничены, выбор меньшей модели учителя может снизить затраты на вывод, при этом обеспечивая эффективные сигналы обучения для модели ученика.

Figure_10
Figure_10

Рассчитайте оптимальную дистилляцию

Целью вычислительно оптимальной дистилляции является определение способа создания модели студента желаемого размера с наименьшей перекрестной энтропией при заданном вычислительном бюджете. В частности, необходимо найти оптимальный объем данных для обучения учащихся, размер модели учителя, данные для обучения, чтобы минимизировать перекрестную энтропию студента и при этом удовлетворить ограничениям вычислительного бюджета.

На рисунке ниже мы видим:

  • Контролируемое обучение всегда соответствует наилучшему варианту настройки дистилляции при достаточном вычислительном бюджете: Контролируемое обучение всегда соответствует наилучшему варианту настройки дистилляции при определенном общем вычислительном бюджете. Это означает, что контролируемое обучение может достичь той же производительности, что и дистилляция, если вычислительный бюджет достаточно велик.

  • Если в вычисления включено обучение учителя, перекрестная энтропия учащихся всегда выше, чем в контролируемой обстановке: это означает, что если вашей единственной целью является создание наилучшей модели с целевым размером и у вас нет доступа к учителю, вам следует выбрать контролируемое обучение вместо обучения учителя и последующей дистилляции. Напротив, если цель состоит в том, чтобы выделить семейство моделей или использовать учителя в качестве обслуживающей модели, то выделение может оказаться более выгодным с вычислительной точки зрения, чем контролируемое обучение.

  • Меньшие модели с большей вероятностью получат выгоду от контролируемого предварительного обучения, в то время как более крупные модели с большей вероятностью получат выгоду от дистилляции: Меньшие модели с большей вероятностью получат выгоду от контролируемого обучения при больших вычислительных бюджетах, в то время как более крупные модели с большей вероятностью получат выгоду от дистилляции при больших вычислительных бюджетах.

Figure_11
Figure_11

На рисунке ниже показаны тенденции изменения оптимального размера учителя и объема обучающих данных по мере изменения вычислительного бюджета. Токены моделей студентов и преподавателей масштабируются по степенному закону, причем токены студентов растут быстрее. Размер лучшей модели учителя сначала увеличивается, пока не станет немного больше ученика, а затем стабилизируется. Это связано с тем, что использование большой модели учителя для вывода обходится дорого, и по мере увеличения количества токенов учеников более эффективным становится переобучение модели учителя.

Figure_12
Figure_12

Ключевые результаты исследования

В результате исследований авторы пришли к следующим выводам:

  1. Предсказуемость производительности через закон масштабирования: Производительность модели-студента размером N_S​, полученной путем дистилляции из модели-учителя размером N_T​ с использованием D_S​ токенов, может быть предсказана с помощью разработанного закона масштабирования дистилляции.

    Практическое значение: Это позволяет заранее оценить, какой результат можно получить от процесса дистилляции, не проводя дорогостоящих экспериментов. Компания может спланировать свои ресурсы и решить, стоит ли вкладываться в дистилляцию, или лучше выбрать другой подход к созданию эффективной модели.

  2. Влияние параметров учителя на студента: Размер модели-учителя NTNT​ и количество токенов для её обучения D_T​ определяют кросс-энтропию модели-учителя L_T=L_T(N_T,D_T), которая, в свою очередь, влияет на кросс-энтропию модели-студента.

    Наглядный пример: Представьте учителя как источник знаний для студента. Если учитель сам недостаточно образован (высокая кросс-энтропия), он не сможет хорошо обучить студента, какими бы способностями студент ни обладал.

  3. Феномен "разрыва в способностях": Исследование выявило интересный эффект - более сильный учитель может привести к худшему студенту, что объясняется "разрывом в способностях" (capacity gap). Влияние кросс-энтропии модели-учителя на потери модели-студента следует степенному закону, который переключается между двумя режимами в зависимости от относительной способности к обучению студента и учителя. Исследование показало, что важен именно разрыв в способности к обучению (гипотезное пространство и оптимизационная способность) между учителем и студентом, а не просто их относительный размер.

    Аналогия для понимания: Представьте, что профессор квантовой физики пытается обучить первоклассника. Несмотря на высокую квалификацию профессора, первоклассник не сможет усвоить сложный материал из-за разрыва в способностях к обучению. Аналогично, если модель-учитель слишком сложна и "мыслит" на уровне, недоступном модели-студенту, эффективность обучения снижается.

  4. U-образная зависимость ошибки студента: Эмпирически подтверждается U-образная зависимость ошибки студента от размера учителя при фиксированном размере студента, что теоретически обосновывается разрывом в емкости между ними.

    Визуальное представление: Если изобразить ошибку студента на графике, где по горизонтальной оси отложен размер учителя, мы увидим U-образную кривую. Это означает, что существует оптимальный размер учителя для данного студента — не слишком маленький (недостаточно знаний) и не слишком большой (слишком сложное представление знаний).

Практические рекомендации

Результаты исследования показывают, что дистилляция становится более эффективной, чем обучение с учителем, при соблюдении следующих условий:

  1. Общее количество вычислений или токенов для студента не превышает пороговое значение, связанное с размером студента, согласно новому закону масштабирования.

    Практический сценарий: Для компании с ограниченным бюджетом на вычисления, которая хочет создать модель размером 1 миллиард параметров, дистилляция может быть оптимальным выбором, если доступно менее 20 миллиардов токенов для обучения (согласно правилу Чинчиллы).

  2. Модель-учитель уже существует, или обучение модели-учителя имеет применение за пределами одной дистилляции.

    Бизнес-кейс: Если компания уже обучила крупную модель для своих основных задач, имеет смысл использовать её для дистилляции меньших, специализированных моделей для развертывания на мобильных устройствах или в средах с ограниченными ресурсами.

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    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 18:18 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 25.10.25 00:49 tyleradams

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  • 25.10.25 00:50 stevekalfman

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  • 25.10.25 05:05 victoriabenny463

    A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)

  • 25.10.25 10:13 wendytaylor015

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  • 25.10.25 10:13 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.10.25 01:03 Christopherbelle

    A terrible financial shock hit me hard. I lost $860,000 in a fake crypto scheme. Things looked good until I tried to cash out my earnings. Suddenly, my account vanished into thin air. I told the police many times, but help never showed up. Despair washed over me; I felt totally beaten. Then, I found Sylvester Bryant Intelligence. Right away, they were skilled and honest about the whole thing. They looked deep into my situation. They tracked where the stolen funds went. They fought hard for me every step of the way. To my great surprise, they got my money back. I thought that was impossible. I owe them so much for their hard work and truthfulness. Sylvester Bryant Intelligence restored my peace. If scams took your crypto, contact them now. Contact Info: Yt7cracker@gmail . com WhatsApp: ‪+1 512 577 7957. or +44 7428 662701.

  • 26.10.25 18:09 victoriabenny463

    A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)

  • 27.10.25 11:15 harristhomas7376

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  • 27.10.25 11:15 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 27.10.25 17:08 raymondgonzales

    Three Cheers for Wizard Hilton Cyber Tech, Bitcoin Savior Extraordinaire In the ever-evolving world of cryptocurrency, where volatility and uncertainty reign supreme, one individual has emerged as a beacon of hope and innovation - Wizard Hilton Cyber Tech, the self-proclaimed "Bitcoin Savior Extraordinaire." This enigmatic figure, with his uncanny ability to navigate the complexities of the digital asset landscape, has captivated the attention of crypto enthusiasts and skeptics alike. Wizard Hilton Cyber Tech journey began as a humble programmer, tinkering with the underlying blockchain technology that powers Bitcoin. But it was his visionary approach and unwavering commitment to the cryptocurrency's potential that propelled him into the limelight. Through a series of strategic investments, groundbreaking algorithmic trading strategies, and a knack for anticipating market shifts, Wizard Hilton Cyber Tech has managed to consistently outperform even the savviest of Wall Street traders. Wizard Hilton Cyber Tech ability to turn even the most tumultuous of Bitcoin price swings into opportunities for substantial gains has earned him the moniker "Wizard," a testament to his unparalleled mastery of the digital currency realm. But Wizard Hilton Cyber Tech impact extends far beyond personal wealth accumulation - Wizard Hilton Cyber Tech has tirelessly advocated for the widespread adoption of Bitcoin, working tirelessly to educate the public, lobby policymakers, and collaborate with industry leaders to overcome the barriers that have long hindered the cryptocurrency's mainstream acceptance. With infectious enthusiasm and boundless energy, Wizard Hilton Cyber Tech has become a true champion of the Bitcoin cause, inspiring a new generation of crypto enthusiasts to embrace the transformative power of this revolutionary technology. As the digital currency landscape continues to evolve, Wizard Hilton Cyber Tech name will undoubtedly be etched in the annals of cryptocurrency history as a visionary, a trailblazer, and, above all, the Bitcoin Savior Extraordinaire. To get your stolen bitcoin back, reach out to Wizard Hilton Cyber Tech via: Email : wizardhiltoncybertech ( @ ) gmail (. ) com WhatsApp number  +18737715701 Good Day.

  • 27.10.25 17:20 fatimanorth

    The Federal Trade Commission said that more than $1 billion had been lost to cryptocurrency scams in 2023. Victims frequently lose everything, including hope, trust, and wealth. When your hard-earned money disappears into digital shadows, you feel trapped. Nowadays, cryptocurrency frauds are very common. You can get help from recovery specialist Marie at [email protected] and via WhatsApp at +1 7127594675.

  • 28.10.25 00:55 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 28.10.25 00:55 elizabethrush89

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  • 29.10.25 03:43 Christopherbelle

    A sudden money crisis struck me. I dropped $82,000 to a phony crypto scam. All seemed fine until I went to pull out my gains. Then, i was unable to get back my hard earned money. I reported it to the police several times. No aid came my way. Deep sadness hit me; I felt crushed. That's when I learned about Sylvester Bryant Intelligence. They acted quick and fair from the start. They checked my case closely. They followed the path of my lost cash. They pushed strong for me at each turn. In shock, they brought my funds back. I had figured it could not happen. I thank them for their effort and honesty. Sylvester Bryant Intelligence gave me calm again. If a scam stole your crypto, reach out to them today. Contact Info: Yt7cracker@gmail . com WhatsApp: +1 512 577 7957 or +44 7428 662701.

  • 29.10.25 10:56 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 29.10.25 10:56 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 30.10.25 09:49 Christopherbelle

    I suffered a huge money blow when $80,000 slipped away in a bogus crypto plot. It all looked great at first. Then I went to pull out my gains, and poof—my account was gone. I kept telling the cops about it, but they did zip. I felt shattered and lost. That's when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed clear steps, sharp know-how, and real drive to fix it. They tracked my missing cash step by step and pushed hard till they got it back. I swear, I figured it was a lost cause. Their straight-up work and trust brought back my calm. If a scam stole your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 30.10.25 12:03 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 31.10.25 13:25 Lillian Lizzy

    THANKS TO THE SERVICES OF THE HACK ANGELS // FOR HELPING ME RECOVER MY USDT AND BTC I lost almost $698,000 in a bitcoin investment scam a few months ago. I was devastated and depressed, and I didn't know what to do. When I saw a favorable review of THE HACK ANGELS RECOVERY EXPERT. I decided to contact them and voice my concerns. God is so good that I am a living testament to the fact that there are still legitimate recovery hackers out there. I will confidently recommend THE HACK ANGELS RECOVERY EXPERT to everyone I meet. I will suggest them to anyone who falls victim to any kind of online scam by using the information below. web: https://thehackangels.com Mail Box; [email protected] WhatsApp; +1(520)-200,2320 If you're in London, you can even visit them in person at their office located at 45-46 Red Lion Street, London WC1R 4PF, UK.

  • 31.10.25 13:25 Lillian Lizzy

    THANKS TO THE SERVICES OF THE HACK ANGELS // FOR HELPING ME RECOVER MY USDT AND BTC I lost almost $698,000 in a bitcoin investment scam a few months ago. I was devastated and depressed, and I didn't know what to do. When I saw a favorable review of THE HACK ANGELS RECOVERY EXPERT. I decided to contact them and voice my concerns. God is so good that I am a living testament to the fact that there are still legitimate recovery hackers out there. I will confidently recommend THE HACK ANGELS RECOVERY EXPERT to everyone I meet. I will suggest them to anyone who falls victim to any kind of online scam by using the information below. web: https://thehackangels.com Mail Box; [email protected] WhatsApp; +1(520)-200,2320 If you're in London, you can even visit them in person at their office located at 45-46 Red Lion Street, London WC1R 4PF, UK.

  • 01.11.25 03:27 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 01.11.25 03:27 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 01.11.25 15:47 kattygates

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  • 01.11.25 15:49 kattygates

    I met an individual on an international dating app, Bumpy. After talking for a few months, the individual encouraged me to start investing on crypto asset trading platform, btc01.org. I started trading and believed I was making profit until I tried to withdraw some of my money, I was asked to pay extra for tax which I did and they kept asking then I knew I have been scammed, I had to contact HACKWEST AT WRITEME DOT COM who then helped to recover the money, the total money I invest is $198,000 in bitcoin. The website is no longer operational. If anyone is in a similar issue, you can as well contact HACK WEST. They also fixed my credit report.

  • 02.11.25 10:55 Christopherbelle

    I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 02.11.25 10:56 Christopherbelle

    I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 02.11.25 15:23 michaeldavenport238

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 02.11.25 15:23 michaeldavenport238

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 04.11.25 04:59 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. [email protected] | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 04.11.25 09:30 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 04.11.25 09:30 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 05.11.25 02:43 jordan_11

    I made a mistake of not researching about their their investment firm(Binary option), it had a lot of promises which made me fall for all their fake promises , after trying to get my withdrawal out from there, I started having a lot of difficulties. Then I contacted their customer support, they only replied a week after and strangely wanted me to make more deposits just to enable my withdrawal, so i started my research of how I could report this treacherous company to the necessary authorities and also maybe i could get back my investment, The only people that were willing to help me out was Treqora Intel, their customer support replied so fast and immediately directed me to their investigative team which took my up my case and started the tracing and reclaim process with swift, after a week i got an email from Treqora Intel stating that a partial amount had been reclaimed, I was so grateful about their help , then I was asked to decide if I wanted a Partial deposit or wanted all my investment reclaimed and sent to me at once, But I was so desperate at the time so I asked that my partial reclaimed ETH be sent to me first , So the deposit took about few minutes before i got it in my wallet and withdrew it. Then my remaining investment took 2 weeks to get back according to their customer support at Treqora Intel. Immediately They got it, I was contacted again Via email that my reclaimed had been fully reclaimed, so grateful till this day to Treqora Intel for taking their time to help me out with what could have been a very depressing moment to me. And yes no upfront payment until the reclaim has been completed and you've been paid fully. Email:support@treqora. com 📱 WhatsApp: ‪‪‪+1 (7 7 3) 9 7 7 - 7 8 7 7‬ ‬‬ 🌐 Website: Treqora. com.

  • 05.11.25 02:44 jordan_11

    Crypto Recovery Services _Hire Treqora Intel

  • 05.11.25 02:48 jordan_11

    Legitimate Crypto Recovery Companies-CONSULT TREQORA INTEL. After falling victim to a crypt0currency scam group, I lost $35,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to rec0vermy stolen funds and I came across a lot of testimonials online about TREQORA INTEL , an agent who helps in rec0ver of lost bitc0in funds, I contacted TREQORA INTEL , and with their expertise, they successfully traced and rec0vered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and rec0very protocols. They are trusted and very reliable with a 100% successful rate record Rec0very bitc0in, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypt0. Email:support@treqora. com Whats_App: ‪‪‪‪‪+1 (7 7 3 ) 9 7 7 - 7 8 7 7‬ ‬‬ ‬‬, Website: Treqora dot com.

  • 05.11.25 16:20 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 05.11.25 16:21 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 07.11.25 02:26 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 07.11.25 09:33 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 07.11.25 16:05 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 07.11.25 23:15 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 07.11.25 23:30 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 07.11.25 23:30 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 07.11.25 23:32 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 07.11.25 23:34 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 09.11.25 03:29 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.11.25 03:29 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 10.11.25 05:06 Christopherbelle

    I lost $52,000 in USDT to a scam. That hit me hard. USDT is a stable cryptocurrency tied to the US dollar. It keeps its value steady. I thought I had found a sure way to grow my money. Things looked good at first. I even built up profits to $120,000. But when I went to pull out my earnings, the platform blocked me. No access. No funds. Panic set in. I felt trapped and helpless. Scams like this target crypto users all the time. They promise quick gains. Then they vanish with your money. Each year, people lose billions to these tricks. I searched for help everywhere. Forums, support groups. Nothing worked. That's when a friend stepped in. He had faced a similar mess before. He told me about Sylvester Bryant. My friend swore by his skills. So I reached out right away. His email is [email protected]. Sylvester Bryant turned it all around. He listened to my story without judgment. His team got to work fast. They started by reviewing every detail of the scam. Step by step, they traced the path of my stolen USDT. They used tools to follow the blockchain. That's the public record of crypto transactions. It shows where funds move. But scammers hide their tracks. Bryant's group dug deep. They contacted exchanges and networks involved. Day after day, they pushed forward. No shortcuts. They kept me updated the whole time. Every email, every call was clear and honest. In the end, they recovered my full amount. That $52,000 came back to me. The process took focus and grit. Bryant's honesty stood out. He charged no hidden fees. Just straight work for results. My stress melted away. I could breathe again. Sleep came easier. My trust in recovery options grew. If a scam has taken your money, act now. Reach out to Sylvester Bryant. He handles cases like this with care. Email him at [email protected]. Or on WhatsApp at +1 512 577 7957 or +44 7428 662701. Don't wait. Get your funds back.

  • 10.11.25 14:28 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 10.11.25 21:52 ashley11

    Legitimate crypto recovery companies in Australia - HIRE TREQORA INTEL

  • 10.11.25 21:53 ashley11

    Legitimate crypto recovery companies in Australia - HIRE TREQORA INTEL Sometimes, life can be unpredictable and present us with unexpected twists and turns. On October 15, 2025, I had an experience that taught me a valuable lesson about the importance of vigilance and caution in the digital age. It began when I met someone on TikTok who claimed to have a surefire way to generate significant profits from Ethereum investments. The individual, who went by the name of Mr. Oscar, presented himself as a financial expert with a proven track record of success. Intrigued by the promise of easy money, I decided to invest a substantial amount of my savings into the Ethereum venture. However, I soon discovered that I had fallen victim to a sophisticated scam. Mr. Oscar had fake credentials and a history of deceiving numerous people, leaving them financially devastated and feeling betrayed, I thought I had lost my investment forever. But I was determined to recover my stolen Ethereum and sought help from a reputable firm specializing in cybersecurity. That's when I stumbled upon Treqora Intel, a company with a stellar reputation for assisting victims of online scams. With the support of Treqora Intel , I was able to recover my lost funds in a remarkably short period. Their team of experts was efficient, responsive, and empathetic, making the recovery process as smooth as possible. I was impressed by their professionalism and commitment to helping individuals like me who have been affected by online scams. This experience has taught me to be more cautious when interacting with strangers online, especially when it comes to investment opportunities that seem too good to be true. It has also reminded me of the importance of verifying the credibility of individuals and companies before making any financial decisions. I am grateful to TREQORA INTEL for their assistance and hope that my story can serve as a warning to others to be vigilant in the online world. By being aware of the potential risks and taking necessary precautions, we can protect ourselves from falling prey to scams and ensure a safer online experience.Email:support@treqora. com Whats_App: ‪‪‪‪‪‪‪+1 (7 7 3 ) 9 7 7 - 7 8 7 7‬‬‬ ‬‬ ‬‬, Website: Treqora. com.

  • 11.11.25 06:47 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 11.11.25 08:34 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.11.25 08:34 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.11.25 08:34 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.11.25 11:15 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 11.11.25 13:36 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 11.11.25 15:16 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 11.11.25 15:36 peggy09

    Crypto theft surges, with billions lost yearly. DIY fixes flop due to tech and legal walls. Standard reports gather dust without pros. Anthony Davies changes that. As the best funds recovery expert, his tracing, partnerships, and methods reclaim hacked wallet assets. He maximizes your shot at getting back stolen cryptocurrency. If you've been hit, reach out to Anthony Davies today. Every minute counts in this fight. Start your recovery journey now—don't let thieves win.Crypto theft surges, with billions lost yearly. DIY fixes flop due to tech and legal walls. Standard reports gather dust without pros. Anthony Davies changes that. As the best funds recovery expert, his tracing, partnerships, and methods reclaim hacked wallet assets. He maximizes your shot at getting back stolen cryptocurrency. If you've been hit, reach out to Anthony Davies today. Every minute counts in this fight. Start your recovery journey now—don't let thieves win. reach him at anthonydaviestech@gmail dot com or telegram anthonydavies

  • 11.11.25 19:28 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.11.25 19:29 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 12.11.25 04:09 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 12.11.25 04:10 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 12.11.25 05:07 peggy09

    Anthony Davies stands out in the world of crypto recovery. His skills come from years of hands-on work with blockchain tech. He helps people get back what thieves took, often against tough odds. i once lost $200000 to a fake broker site, anthony stood out as the only person who was able to get back my funds. you can contact him by sending an email to; anthonydaviestech @ gma1l com

  • 12.11.25 09:37 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 12.11.25 09:37 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 13.11.25 19:01 peggy09

    i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com

  • 13.11.25 20:05 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 13.11.25 20:05 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 13.11.25 22:51 ashley11

    Recover All Lost Cryptocurrency From Scammers

  • 13.11.25 22:52 ashley11

    Recover All Lost Cryptocurrency From Scammers TREQORA INTEL has exhibited unparalleled strength in the realm of recovery. They stand out as the premier team to collaborate with if you encounter withdrawal difficulties from the platform where you’ve invested. Recently, I engaged with them to recover over a million dollars trapped in an investment platform I’d been involved with for months. I furnished their team with every detail of the investment via Email (SUPPORT @ TREQORA . C O M”), including accounts, names, and wallet addresses to which I sent the funds. This decision proved to be the best I’ve made, especially after realizing I had been sc**med by the company. Initially, I harbored doubts about their services, but I was proven wrong. TREQORA INTEL ensures exemplary service delivery and ensures the perpetrators face justice. They employ advanced techniques to ensure you regain access to your funds. Understandably, many individuals who have fallen victim to investment scams may still harbor trepidation about engaging in online services again due to the trauma of being sc**med. However, I implore you to take action. Seek assistance from TREQORA INTEL today and witness their remarkable capabilities firsthand. Among the myriad of hackers available, TREQORA INTEL stands head and shoulders above the rest. While I may not have sampled all of them, the few I attempted to work with previously were unhelpful and solely focused on depleting the little funds I had left. I am grateful that I resisted their enticements, and despite the time it took me to discover TREQORA INTEL, they ultimately fulfilled my primary objective. I am confident they will execute the task proficiently. Without their intervention, I would have remained despondent and perplexed indefinitely. Don’t make the error of entrusting sc**mers to rectify a sc*m; the consequences are evident. Email:support@treqora. com,WhatsApp: ‪‪‪‪‪‪+1 (7 7 3) 9 7 7 - 7 8 7 7‬‬‬‬ ‬‬,Website: Treqora. com. How Can I Recover My Lost Bitcoin From A Romance Scammer-HIRE TREQORA INTEL

  • 13.11.25 23:36 daisy

    i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com

  • 14.11.25 03:42 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.11.25 03:42 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.11.25 08:38 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 14.11.25 10:39 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 14.11.25 12:12 daisy

    i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com

  • 14.11.25 15:07 caridad

    Perth Family Saved After $400K Crypto Scam Our family in Perth, WA invested through what we thought was a trusted platform but ended up being a fraudulent investment scheme. We lost nearly AUD 420,000 worth of BTC and USDT. Luckily, a friend recommended Bitreclaim.com. Their 24/7 customer support assigned us a smart contract audit specialist who asked for wallet addresses and transaction hashes. With their forensic blockchain trace, they recovered over 5.1 BTC directly into our hardware wallet. For Perth investors: don’t give up hope. Submit a case at Bitreclaim.com immediately. Their professionalism and success rate in Australia is unmatched.

  • 14.11.25 18:33 justinekelly45

    FAST & RELIABLE CRYPTO RECOVERY SERVICES Hire iFORCE HACKER RECOVERY I was one of many victims deceived by fake cryptocurrency investment offers on Telegram. Hoping to build a retirement fund, I invested heavily and ended up losing about $470,000, including borrowed money. Just when I thought recovery was impossible, I found iForce Hacker Recovery. Their team of crypto recovery experts worked tirelessly and helped me recover my assets within 72 hours, even tracing the scammers involved. I’m deeply thankful for their professionalism and highly recommend their services to anyone facing a similar situation.  Website: ht tps://iforcehackers. co m WhatsApp: +1 240-803-3706   Email: iforcehk @ consultant. c om

  • 14.11.25 20:56 juliamarvin

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  • 15.11.25 12:47 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 15.11.25 14:39 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.11.25 14:39 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.11.25 15:31 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 15.11.25 15:52 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 16.11.25 14:43 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 16.11.25 14:44 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 16.11.25 20:38 [email protected]

    A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.

  • 03:24 johnny231

    INFO@THEBARRYCYBERINVESTIGATIONSDOTCOM is one of the best cyber hackers that i have actually met and had an encounter with, i was suspecting my partner was cheating on me for some time now but i was not sure of my assumptions so i had to contact BARRY CYBER INVESTIGATIONS to help me out with my suspicion. During the cause of their investigation they intercepted his text messages, social media(facebook, twittwer, snapchat whatsapp, instagram),also call logs as well as pictures and videos(deleted files also) they found out my spouse was cheating on me for over 3 years and was already even sending nudes out as well as money to anonymous wallets,so i deciced to file for a divorce and then when i did that i came to the understanding that most of the cryptocurrency we had invested in forex by him was already gone. BARRY CYBER INVESTIGATIONS helped me out through out the cause of my divorce with my spouse they also helped me in retrieving some of the cryptocurrency back, as if that was not enough i decided to introduce them to another of my friend who had lost her most of her savings on a bad crytpo investment and as a result of that it affected her credit score, BARRY CYBER INVESTIGATIONS helped her recover some of the funds back and helped her build her credit score, i have never seen anything like this in my life and to top it off they are very professional and they have intergrity to it you can contact them also on their whatsapp +1814-488-3301. for any hacking or pi jobs you can contact them and i assure you nothing but the best out of the job

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